I also don't think you can separate genetic influences from environmental influences, i.e. one allele might make you do well in one environment and poorly in a different environment. This appears to the case for the 7R allele of the DRD4 gene: http://www.northwestern.edu/newscenter/stories/2008/06/ariaa...
I also don't think any genes actually code for intelligence as it's commonly understood. Intelligence is, basically, knowledge (including knowledge about how to acquire knowledge). Genes affect brain chemistry, which influences intelligence in different ways, within a given environment.
> Intelligence tests and psychometrics have generally found high correlations between different aspects of intelligence, rather than the low correlations which Gardner's theory predicts, supporting the prevailing theory of general intelligence rather than multiple intelligences (MI).[19] The theory has been widely criticized by mainstream psychology for its lack of empirical evidence, and its dependence on subjective judgement.[20]
As for your other points...
> I also don't think you can separate genetic influences from environmental influences, i.e. one allele might make you do well in one environment and poorly in a different environment.
That's probably the case for some genes, sure. But finding strong correlations between twins raised apart would seem to indicate that many of the genetic factors are not entirely environment-sensitive.
> I also don't think any genes actually code for intelligence as it's commonly understood. Intelligence is, basically, knowledge (including knowledge about how to acquire knowledge). Genes affect brain chemistry, which influences intelligence in different ways, within a given environment.
Twin studies seem to contradict this. From Wikipedia (heritability of IQ [1])
* Identical twins—Reared together .86
* Identical twins—Reared apart .76
So yes, environment has an impact, but there's still a high degree of correlation in intelligence between identical twins raised apart.
[1] https://en.wikipedia.org/wiki/Heritability_of_IQ#Correlation...
In an modern developed economy, where you'll be more likely to do well if your IQ is high, some people will have inherited alleles which tend to raise their IQs and make them well-adapted to their environment, others different alleles which make them poorly adapted.
And, on top of that, there's an environmental, or rather cultural component.